Re: polygon area

I went there and I found this:Even Tandog has a trick formula for polygon areas. There's also an extract from Shakespeare's long forgotten play Henry X11 part 5 and finally... the secret identites of the superheros are revealed.

Re: polygon area

The Shakespeare thing was basically the trigonometric way of working put the area of a triangle, put into the form of an old-fashioned poem. I would put it here, but as my room is currently a complete mess I can't seem to find the book at the moment.

Edit: I found it!

If a triangle has no right angle,And the area needs to be seen,Multiply half by two of the sides,And the sin of the angle between.

There's a little treat for anyone who likes browsing through old topics.

Re: polygon area

John, if you take any polygon and draw lines from the vertices to the center you will get n equal triangles with bases the length s and a vertice angle of 360/n°. Since the height of any given triangle is s/2tan(180/n) the area of any triangle there will be;

A = (s/2) [s/2tan(180/n)] = s²/(4tan[180/n])

So the total area is number of sides times the area of any of the triangles which gives the formula you have above. But there was no calculus needed.